Swarming, or aggregations of organisms in groups, can be found in nature in many organisms ranging from simple bacteria to mammals. Such behavior can result from several different mechanisms. For example, individuals may respond directly to local physical cues such as concentration of nutrients or distribution of some chemicals as seen in some bacteria and social insects, or they may respond directly to other individuals as seen in fish, birds, and herds of mammals. In this dissertation, we

Abstract-In this article we specify an -member "individual-based" continuous time swarm model with individuals that move in an -dimensional space according to an attractant/repellent or a nutrient profile. The motion of each individual is determined by three factors: i) attraction to the other individuals on long distances; ii) repulsion from the other individuals on short distances; and iii) attraction to the more favorable regions (or repulsion from the unfavorable regions) of the attractant/repellent profile. The emergent behavior of the swarm motion is the result of a balance between inter-individual interactions and the simultaneous interactions of the swarm members with their environment. We study the stability properties of the collective behavior of the swarm for different profiles and provide conditions for collective convergence to more favorable regions of the profile.

Swarming, or aggregations of organisms in groups, can be found in nature in many organisms ranging from simple bacteria to mammals. Such behavior can result from several different mechanisms. For example, individuals may respond directly to local physical cues such as concentration of nutrients or distribution of some chemicals as seen in some bacteria and social insects, or they may respond directly to other individuals as seen in fish, birds, and herds of mammals. In this dissertation, we

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